What's the purpose of killing the tiger?*
Is it supposed to be a deterrent, so that other tigers know who's boss and don't do the same in future? Do we need to exact retribution upon the tiger, so that it "deservedly suffers" for the crime that it committed? Is killing the tiger going to repair any of the damage that it caused?*These are the three of the main reasons why we punish those who do something wrong; deterrence, retribution and reparation. *And I think it's quite obvious that none of them apply in these circumstances, to a tiger who has killed simply by acting on instinct.
*
The only other valid reason I can think of for carrying out a punishment is prevention. That is, if*it was a case of killing the tiger whilst it was attacking the woman in order to save the woman's life, that's fair enough. Or if the only way to stop this particular tiger from going on a rampage and killing everyone else too is to kill it first, that's also fair enough. Although again, this is not applicable in this case.
So I don't really see the need to kill the tiger. Even if we kill it, there are thousands of other tigers just like it, who would have done exactly the same thing in that situation, that we're doing nothing about. The best thing to do is just release it into the wild amongst other tigers, far from humans, where it can kill as many gazelles as it likes. Or keep it contained, away from the public so that it can't hurt anyone else.*